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How many one-to-one correspondences are there between two sets with
a. 6 elements each?
b. d elements each? Explain your reasoning.
a. There are 720 one-to-one correspondences between two sets with 6 elements each.
b. There are
one-to-one correspondences between two sets with d elements each. For the first element of the first set, there are
elements of the second set it can be paired with. After that, for the second element of the first set, there are elements of the second set it can be paired with. The process
continues. These numbers of possibilities are
together to get the total number of one-to-one correspondences.
(Simplify your answers.)